Lung-DDPM+: Efficient Lung CT Synthesis

• The paper extends DDPM by integrating semantic lesion masks and high-order ODE-based sampling, achieving up to 14× faster and memory-efficient lung CT synthesis.
• It utilizes patch-wise training and coordinate embeddings to reduce GPU memory usage nearly 7× while preserving multi-scale anatomical features in synthetic outputs.
• Quantitative evaluations reveal improved segmentation metrics and a Visual Turing Test that confirms high clinical plausibility for data augmentation in lung image analysis.

Lung-DDPM+ is a family of diffusion probabilistic models specializing in anatomically faithful and computationally efficient synthesis of lung medical images, most notably thoracic CT scans depicting lung nodules. Developed as an extension and refinement of prior denoising diffusion probabilistic models (DDPMs) for medical image synthesis, Lung-DDPM+ integrates semantic lesion guidance, memory-efficient patch-wise strategies, and high-order sampling accelerators. These enhancements enable the generation of high-quality and faithful synthetic datasets under marked compute and memory constraints, supporting data augmentation and addressing data scarcity in lung image analysis and segmentation tasks (Jiang et al., 12 Aug 2025, Khadra et al., 16 Oct 2024, Mahaulpatha et al., 3 Jan 2024).

1. Diffusion Model Foundations and Architecture

Lung-DDPM+ is based on the DDPM paradigm, which defines a forward noising Markov process $$q(x_t|x_{t-1}) = \mathcal{N}(x_t; \sqrt{1-\beta_t} x_{t-1}, \beta_t I)$$ and learns a reverse process $$p_\theta(x_{t-1}|x_t) = \mathcal{N}(x_{t-1}; \mu_\theta(x_t, t), \Sigma_\theta(t))$$ that incrementally reconstructs data samples from Gaussian noise. The simplified training objective, as in Ho et al., is a mean-squared error (MSE) between actual and predicted noise, typically written as

$$L(\theta) = \mathbb{E}_{x_0, \epsilon \sim \mathcal{N}(0,I), t}\left[ \|\epsilon - \epsilon_\theta(\sqrt{\bar \alpha_t} x_0 + \sqrt{1-\bar \alpha_t} \epsilon, t)\|^2 \right],$$

where $\epsilon_\theta$ is the neural denoiser, $\beta_t$ is the noise schedule (usually linear or cosine), and $\bar\alpha_t = \prod_{i=1}^t (1-\beta_i)$ (Jiang et al., 12 Aug 2025, Khadra et al., 16 Oct 2024, Mahaulpatha et al., 3 Jan 2024).

Core to its architecture is a U-Net backbone, adapted as a 2D or 3D residual network depending on the application domain. For CT, this typically involves a 3D U-Net, operating on sub-volumes or patches, with input features augmented by lesion or nodule segmentation masks and coordinate encodings. Skip connections and residual blocks are employed to preserve multi-scale anatomical features, while sinusoidal timestep embeddings provide time conditioning essential for the diffusion schedule.

2. Semantic Guidance and Mask Conditioning

A key innovation in Lung-DDPM+ is explicit control over synthetic lesion (e.g., nodule) geometry and placement via binary semantic layout masks. During both training and inference, the nodule mask $m$ is concatenated as an input channel to the U-Net, ensuring that generated samples respect anatomical and pathological priors, such as exact spatial nodule positioning within lung parenchyma (Jiang et al., 12 Aug 2025, Khadra et al., 16 Oct 2024). This conditioning strategy enforces geometric constraints on the output, improves clinical plausibility, and addresses challenges of anatomical imprecision previously observed in unconditional synthesis.

Channel-wise mask concatenation is sufficient due to the low spatial complexity of binary segmentation masks, but more complex fusion (e.g., adaptive group normalization or cross-attention) is possible if greater flexibility is required (Jiang et al., 12 Aug 2025).

3. Sampling Acceleration via DPM-Solver and Memory Efficiency

Standard DDPM sampling is computationally expensive, typically requiring $O(10^3)$ neural network evaluations per sample. Lung-DDPM+ integrates an accelerated Pulmonary DPM-Solver, a high-order ODE-based integrator derived from DPM-Solver++ [Lu et al.], which reduces function evaluations dramatically (e.g., from hundreds to 10–20), yielding up to 14-fold faster sampling and 8-fold reduction in FLOPs compared to predecessor models. The ODE approach approximates the probability flow equation with high-order Taylor expansions, allowing larger time steps while maintaining image fidelity (Jiang et al., 12 Aug 2025).

For further efficiency, memory-constrained implementations rely on patch-wise training, where the U-Net denoises small random 3D patches (e.g., $64\times64\times64$ voxels) extracted from larger CT volumes, coupled with coordinate embeddings to preserve spatial context. At inference, these patch-based networks are capable of reconstructing anatomically coherent whole volumes (Khadra et al., 16 Oct 2024). This strategy yields a minimum 4-fold reduction in memory versus full-volume DDPMs and enables training on commodity GPUs.

The table below summarizes the primary efficiency gains achieved by Lung-DDPM+ (Jiang et al., 12 Aug 2025, Khadra et al., 16 Oct 2024):

Efficiency Metric	Legacy DDPM	Lung-DDPM+	Speedup/Reduction
TFLOPs/sample (128³)	4.35	0.54	8× fewer
GPU memory (GB)	~6.2	0.91	6.8× lower
Sampling time (s/sample)	~53	3.8	14× faster

4. Quantitative Evaluation and Clinical Validation

Lung-DDPM+ is evaluated on the public LIDC-IDRI dataset and related CT collections, with both segmentation accuracy and perceptual fidelity as key endpoints. When used to augment training data for 3D and 2D U-Net segmenters, the addition of Lung-DDPM+ synthetic scans significantly improves Dice coefficient (3D Dice: 0.48 to 0.56; 2D Dice: 0.019 to 0.45, with HD95 improved from ~55 mm to ~25 mm), outperforming traditional affine/noise augmentation (Jiang et al., 12 Aug 2025, Khadra et al., 16 Oct 2024). Synthetic-only nnU-Net models trained on Lung-DDPM+ images attain Dice scores equivalent to or exceeding the real-only baselines (Dice = 0.5016 vs. 0.4913), further evidencing the utility of DDPM-based synthetic data for segmentation.

Clinical plausibility is validated through a Visual Turing Test, where radiologists are unable to reliably discriminate between real and synthetic nodule volumes (identification accuracy 63.9%, close to chance), indicating a high level of anatomical fidelity in Lung-DDPM+ outputs (Jiang et al., 12 Aug 2025).

5. Comparison with Related Diffusion Methods

Lung-DDPM+ shares foundational infrastructure with other medical image DDPMs but incorporates domain-specific advances to meet the anatomical and efficiency demands of thoracic CT synthesis:

• Unlike unconditional or simply classifier-free guidance approaches, Lung-DDPM+ is explicitly conditioned on spatial masks, controlling not just pathology presence but its exact placement and morphology (Mahaulpatha et al., 3 Jan 2024, Jiang et al., 12 Aug 2025).
• Compared to general fast-sampling strategies for medical DDPMs (e.g., DPM-Solver-3 in (Xia et al., 2022)), the Pulmonary DPM-Solver in Lung-DDPM+ is tailored to the anatomical heterogeneity and region-of-interest specificity required for nodule synthesis.
• Multi-conditioned DDPMs and ILVR-like frameworks (Krishna et al., 7 Sep 2024) utilize low-pass guidance maps or multi-modal inputs for controlled sampling, but Lung-DDPM+ leverages explicit, binary lesion layouts for fine-grained anatomical supervision.
• Patch-wise design and coordinate conditioning distinguishes Lung-DDPM+ from monolithic 3D DDPMs, reducing memory/compute load and facilitating scale-up without loss of local-global anatomical coherence (Khadra et al., 16 Oct 2024).

6. Extensions, Limitations, and Future Directions

Lung-DDPM+ generalizes beyond lung nodules to tumors, lesions, and possibly paired multi-modality synthesis (e.g., CT and X-ray), contingent on availability of high-quality masks or derived layouts. Potential applications include data augmentation for rare thoracic diseases, cross-domain image translation, and real-time edge deployment for imaging workflows (Jiang et al., 12 Aug 2025, Mahaulpatha et al., 3 Jan 2024).

Current limitations include reliance on expert-annotated or rule-based layout masks, sensitivity to domain shifts across scanners or CT protocols, and occasional over-segmentation when synthetic nodules lack real CT texture detail. Proposed directions involve incorporating unpaired lesion data via cycle-consistency objectives, adaptive mask sampling, integration of clinical metadata, and progressive latent-space diffusion for higher resolutions and reduced memory footprints (Jiang et al., 12 Aug 2025, Khadra et al., 16 Oct 2024, Mahaulpatha et al., 3 Jan 2024).

7. Summary

Lung-DDPM+ defines the state of the art in efficient, mask-controlled, and anatomically faithful synthetic lung image generation. By uniting structured semantic guidance, high-order ODE-based sampling, and patch-wise memory efficiency, it provides a scalable solution to medical image scarcity, supporting downstream segmentation and diagnostic model development with measurable clinical utility (Jiang et al., 12 Aug 2025, Khadra et al., 16 Oct 2024, Mahaulpatha et al., 3 Jan 2024).